Every time I try to select a single object, it selects everything in the scene. How do I separate them?
I think the problem you have is that you added the cube in the edit mode of the character(?). This results in the cube being a part of the character object.
If you really want to have seperate OBJECTS (not only meshes), you have to add the cube in Object Mode. (Mode selection is on the bottom-left corner of the 3d editor).
Another way is to seperate the meshes by selecting the part of the mesh you want to have in a seperate object and pressing P and clicking selection